Expectation of integral of a stochastic process

112 Views Asked by At

Let $r_t$ be governed by a mean reverting process:

$dr_t = K(\theta - r_t)dt + \sigma dW_t $

where $W_t $ is standard weiner process, and $\sigma , K, \theta$ are constants

Can it be shown that $-log (E[e^{-\int r_sds}]) = \theta (T- \frac{(1- e^{-KT})}{K}) + r_o \frac{(1- e^{-KT})}{K} $